Legendre-tau-Galerkin and spectral collocation method for nonlinear evolution equations

Qin, Yonghui; Ma, Heping

doi:10.1016/j.apnum.2020.02.001

Cited by 8 publications

(1 citation statement)

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“…As consequence of the union of the KdV and Burgers equations arise the KdVB equation, which in our case has homogeneous non-periodic boundary conditions. From a numerical point of view, KdVB-type equations with constant coefficients have been widely studied by means of different methods; see for instance the works [31,37,11,23,27,28] and references therein for more details.…”

Section: Methods and Theoretical Resultsmentioning

confidence: 99%

A numerical study of third-order equation with time-dependent coefficients: KdVB equation

Montoya¹

2020

Preprint

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In this article we present a numerical analysis for a third-order differential equation with non-periodic boundary conditions and time-dependent coefficients, namely, the linear Korteweg-de Vries Burgers equation. This numerical analysis is motived due to the dispersive and dissipative phenomena that government this kind of equations. This work builds on previous methods for dispersive equations with constant coefficients, expanding the field to include a new class of equations which until now have eluded the time-evolving parameters. More precisely, throughout the Legendre-Petrov-Galerkin method we prove stability and convergence results of the approximation in appropriate weighted Sobolev spaces. These results allow to show the role and trade off of these temporal parameters into the model. Afterwards, we numerically investigate the dispersion-dissipation relation for several profiles, further provide insights into the implementation method, which allow to exhibit the accuracy and efficiency of our numerical algorithms.

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